Step 1Peel 1 lemon with a vegetable peeler, taking care not to cut into the bitter white pith. Place the peel in a nonreactive medium saucepan with the crushed cardamom, half-and-half and sugar. Scrape the vanilla pod seeds into the pan and drop in the pod. Heat over high heat to just under a boil. Remove from the heat, and allow to steep for 10 to 15 minutes.
Step 2In a medium mixing bowl, whisk the egg yolks, and then pour in some of the hot half-and-half mixture, stirring constantly. Pour the mixture back into the pan and cook over medium heat, stirring constantly, until it coats the back of a wooden spoon, 4 to 5 minutes.
Step 3Pour the mixture through a strainer into a bowl. Finely grate the zest of 2 lemons and add it to the mixture. Allow to stand for 10 minutes.
Step 4Add the cream to the mixture. Juice all 5 lemons and add the juice (you should have about three-fourths cup) to the cream mixture. Chill thoroughly.
Step 5Freeze in an ice cream machine according to the manufacturer's instructions. (Makes 1 quart.)